Emergent Metric Space-Time from Matrix Theory

TL;DR

This paper explores how the IKKT matrix model can produce an emergent, continuous, and flat space-time with expanding three-dimensional space, providing insights into early universe cosmology and dimensional stabilization.

Contribution

It proposes a new emergent metric within the matrix model and demonstrates how a realistic cosmological evolution can arise from it.

Findings

Emergent space-time is continuous and infinite in extent.

The model shows a transition from a string phase to a classical universe.

Three spatial dimensions expand and evolve like a radiation-dominated universe.

Abstract

The IKKT matrix model yields an emergent space-time. We further develop these ideas and give a proposal for an emergent metric. Based on previous numerical studies of this model, we provide evidence that the emergent space-time is continuous and infinite in extent, both in space and in time, and that the metric is spatially flat. The time evolution describes the transition from a string-theoretic emergent phase to a phase in which the $SO(9)$ symmetry of the model is spontaneously broken to $SO(6) \times SO(3)$, with three dimensions of space expanding, becoming classical and at later times evolving like in a radiation-dominated universe, and the remaining six dimensions of space stabilized at the string scale. We speculate on how this analysis can be extended to yield an early universe cosmology which, in addition to the above-mentioned properties, also leads to a roughly scale-invariant spectrum of cosmological fluctuations and gravitational waves.